Sync data off of broken iPhone

I recently broke my iPhone by dropping it and since I can't get past the "Unlock" screen, I obviously can't open the ToodleDo app. I haven't synced with the web server in at least a week since it is a US phone but I am in Taiwan so I don't get cellular data and WiFi is not easy for me to access. Since it doesn't look like I'll be able to use my iPhone any more, is there any way I can sync the data onto the web server or even to my computer through iTunes (which I can still sync my iPhone with)? Or am I stuck with all the changes since I last synced inaccessible forever?

Unfortunately, the only way to sync the app is to run the app and allow it to sync. The other thing you could do is back up the entire phone to iCloud or iTunes and then restore it to a new iPhone. You can then open the app on the new iPhone and it will sync.

Not the end of the world for me. I figured just as much but thought asking it here was worth a shot. But a lot of stuff is backed up, just not the recent stuff, so I'll manage. I don't think my situation is common, but perhaps you could make a feature kind of like the Find my iPhone app (which I haven't used), that syncs from the webpage rather than the iPhone itself.